한국컴퓨터정보학회논문지 (Journal of the Korea Society of Computer and Information)

  • 제29권11호
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  • Pages.97-105
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  • 2024
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  • 1598-849X(pISSN)
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  • 2383-9945(eISSN)
한국컴퓨터정보학회 (Korean Society of Computer Information)
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A Review of Topological Deep Learning Focused on Simplicial Complex and Cell Complex

  • Ho-Sik Seok (Dept. of Artificial Intelligence and Data Science, Korea Military Academy)
  • 투고 : 2024.10.24
  • 심사 : 2024.11.18
  • 발행 : 2024.11.29
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⟨ 이전 논문 다음 논문 ⟩

초록

화학 반응이나 경제 현상을 모델링할 때는 개체 간의 상호작용을 표현해야 한다. 상호작용의 분석이 필요한 도메인에서 그래프 뉴럴 네트워크를 활발히 적용하고 있으나, 데이터에 존재하는 위상 구조를 표현하는 과정에서 그래프 뉴럴 네트워크의 표현 능력이 충분하지 않다고 알려져 있다. 데이터에 존재하는 위상 구조를 활용하는 토폴로지 데이터 분석(TDA)과 딥러닝을 결합한 토폴로지 딥러닝(TDL)은 복잡한 관계를 내포한 데이터의 분석 및 표현에 강점이 있는데, 본 논문에서는 특히 단체 복합체(simplicial complex)와 셀 복합체(cell complex)에 주목하여 토폴로지 딥러닝의 주요 접근법을 소개하고자 한다. 본 논문에서는 단체 복합체와 셀 복합체를 이해하는 과정에서 요구되는 기본 개념과 주요 접근법을 요약 소개하여 토폴로지 딥러닝을 응용하려는 연구자에게 도움을 제공하고자 한다.

Lots of tasks including physical systems modeling, chemical reaction prediction, and relation extraction require dealing with higher-order relations. Graph neural networks (GNNs) are favorite models for relational data but they have inherent limits due to their focus on pairwise relationships. Topological data analysis (TDA) provides insight into the "shape" of data (or underlying data topology). TDA aims to infer information about data manifold such as connectivity and offers higher-dimensional analog of graphs. Topological deep learning (TDL) combines various deep learning techniques with TDA. TDL enables us to formulate simplicial complex and cell complex through techniques such as low-dimensional embedding and attention. In this paper, we summarize recent achievements especially on simplicial complex and cell complex. We also provide succinct descriptions of related concepts.

키워드

과제정보

This study was supported by research fund of Korea Military Academy(Future Strategy and Technology Research Institute). (RN: 24-AI-Center-03).

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